In an 8- to 10-inch frying pan over high heat, bring bourbon to a simmer. Remove from heat, carefully ignite with a match (not beneath or near a fan, vent, or flammables), and shake pan gently until flame dies. Set aside.
In a 3- to 4-quart pan over high heat, stir milk with sugar until simmering. Remove from heat and whisk some of the hot liquid into yolks; then return mixture to pan.
Stir over low heat until custard coats the back of a spoon in a smooth, velvety layer, 6 to 9 minutes.
Remove from heat and stir in whipping cream, bourbon, and nutmeg. Pour mixture through a fine strainer into a large metal bowl; discard residue. Nest bowl of custard in ice and stir often until the mixture is cold, about 15 minutes.
Pour custard into an ice cream maker and freeze, following manufacturer's directions or until dasher is hard to turn.
Serve or, for firmer ice cream, store airtight in freezer at least 3 hours (or up to 1 week).
Nutritional analysis does not include Hazelnut Caramel Sauce.